Application of conservation laws to derivation of conditions of stability for stationary flows of an ideal fluid

1987 ◽  
Vol 28 (3) ◽  
pp. 351-358 ◽  
Author(s):  
V. A. Vladimirov
Keyword(s):  
Conservation Laws ◽  
Ideal Fluid ◽  
Stationary Flows ◽  
Conditions Of Stability

scholarly journals The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids

2020 ◽  
Vol 476 (2239) ◽  
pp. 20190851
Author(s):  
Thomas Machon
Keyword(s):  
Conservation Laws ◽  
Steady Flow ◽  
Ideal Fluid ◽  
Higher Order ◽  
Vorticity Field ◽  
Vortex Lines ◽  
Type Invariant ◽  
Ideal Fluids ◽  
Topological Obstruction

If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV ≠ 0 gives both a global topological obstruction to steady flow and, in a particular form, a local obstruction. GV is interpreted as helical compression and stretching of vortex lines. Examples are given where the value of GV is determined by a set of distinguished closed vortex lines.

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws
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